MATH YUP 4. (please answer correct question and make answer clear)

4. [-14.28 Points] DETAILS ASWMSCI15 5.E.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER In a gambling game, Player A and Player B both have a $5 and a $20 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. (a) Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Player B $5 $20 $5 Player A $20 (b) Is there a pure strategy? Why or why not? and the minimum of the column maximums is ---Select--- . Since the maximum of the row minimums is --Select- (c) Determine the optimal strategies and the value of this game. probability Player A selects $5 probability Player A selects $20 probability Player B selects $5 probability Player B selects $20 Does the game favor one player over the other? O Yes O No (d) Suppose Player decides to deviate from the optimal strategy and begins playing each bill 50% of the time. What should Player A do to improve Player A's winnings? and select $20 with probability If Player B begins playing each bill 50% of the time, Player A should instead select $5 with probability Comment on why it is important to follow an optimal game theory strategy. Following the optimal strategy ---Select--- other players from taking advantage of the strategy you're playing, since they cannot improve their expected payout by not playing the optimal strategy